GATE 2010 CE Question Paper

⏐CE⏐ GATE 2010 www.gateforum.com

Q. No. 1 – 25 Carry One Mark Each

⎡2 ⎤
sin ⎢ x ⎥
1. The lim ⎣ 3 ⎦ is
x →0 x

(A) 2 (B) 1 (C) 1 (D) 1
3 4 2

2. Two coins are simultaneously tossed. The probability of two heads simultaneously
appearing is

(A) 1 (B) 1 (C) 1 (D) 1
8 6 4 2

3. The order and degree of the differential equation
3
d3 y ⎛ dy ⎞ 2
3
+4 ⎜ ⎟ + y = 0 are respectively
dx ⎝ dx ⎠
(A) 3 and 2 (B) 2 and 3 (C) 3 and 3 (D) 3 and 1

4. Two people weighing W each are sitting on a plank of length L floating on water
at L from either end. Neglecting the weight of the plank, the bending moment
4
at the centre of the plank is
WL WL WL
(A) (B) (C) (D) zero
8 16 32

5. For the truss shown in the figure, the force in the member QR is

Q
R

L
T
S
L
P
(A) Zero (B) P (C) P (D) 2 P
2

6. The major and minor principal stresses at a point are 3MPa and -3MPa
respectively. The maximum shear stress at the point is
(A) Zero (B) 3MPa (C) 6MPa (D) 9MPa

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7. The number of independent elastic constants for a linear elastic isotropic and
homogeneous material is
(A) 4 (B) 3 (C) 2 (D) 1

8. The effective length of a column of length L fixed against rotation and translation
at one end and free at the other end is
(A) 0.5 L (B) 0.7 L (C) 1.414 L (D) 2L

9. As per India standard code of practice for pre stressed concrete (IS:1343-1980)
the minimum grades of concrete to be used for post-tensioned and pre-tensioned
structural elements are respectively
(A) M20 for both (B) M40 and M30 (C) M15 and M20 (D) M30 and M40

10. A solid circular shaft of diameter d and length L is fixed at one end and free at
the other end. A torque t is applied at the free end. The shear modulus of the
material is G. The angle of twist at three free ends is
16TL 32TL 64TL 128TL
(A) (B) (C) (D)
π d4G π d4G π d4G π d4G

11. In a compaction test, G, w, S and e represent the specific gravity, water content,
degree of saturation and void ratio of the soil sample, respectively. If γw
represents the unit weight of water and γw represents the dry unit weight of the
soil, the equation for zero air voids line is
Gγ w Gγ w Gγ w Gw
(A) γ d (B) γ d (C) γ d (D) γ d
1 + Se 1 + Gw e + γ wS 1 + Se

12. A fine grained soil has liquid limit of 60 and plastic limit of 20. As per the
plasticity chart, according to IS classification, the soil is represented by the letter
symbols
(A) CL (B) CI (C) CH (D) CL-ML

13. Quick sand condition occurs when
(A) The void ratio of the soil becomes 1.0
(B) The upward seepage pressure in soil becomes zero
(C) The upward seepage pressure in soil becomes equal to the saturated unit
weight of the soil
(D) The upward seepage pressure in soil becomes equal to the submerged unit
weight of the soil



14. The e-log p curve shown in the figure is representative of
(A) Normally consolidated clay

Void ratio, e
(B) Over consolidated clay

(C) Under consolidated clay

(D) Normally consolidated clayey sand
log p

15. If σh , σv , σh , and σv represent the total horizontal stress, total vertical stress,
effective horizontal stress and effective vertical stress on a soil element,
respectively, the coefficient of earth pressure at rest is given by
σh σh σv σv
(A) (B) (C) (D)
σv σ 'v σh σ 'h
16. A mild-sloped channel is followed by a steep-sloped channel. The profiles of
gradually varied flow in the channel are
(A) M3 , S2 (B) M3 , S3 (C) M2 , S1 (D) M2 , S2

17. The flow in a rectangular channel is subcritical. If width of the channel is reduced
at a certain section, the water surface under no-choke condition will
(A) Drop at a downstream section (B) Rise at a downstream section
(C) Rise at an downstream section (D) Not undergo any change

18. The correct match of Group-I with Group-II is
Group-II Group-II
P. Evapotranspiration 1. Penman method
Q. Infiltration 2. Snyder’s method
R. Synthetic unit hydrograph 3. Muskingum method
S. Channel Routing 4. Horton’s method
(A) P-1, Q-3, R-4, S-2 (B) P-1, Q-4, R-2, S-3
(C) P-3, Q-4, R-1, S-2 (D) P-4, Q-2, R-1, S-3

19. Group-I gives a list of devices and Group-II gives the list of uses

P. Pitot tube 1. Measuring pressure in a pipe
Q. Manometer 2. Measuring velocity of flow in a pipe
R. Venturimeter 3. Measuring air and gas velocity
S. Anemometer 4. Measuring discharge in a pipe



The correct match of Group-I with Group-II is
(A) P-1, Q-2, R-4, S-3 (B) P-2, Q-1, R-3, S-4
(C) P-2, Q-1, R-4, S-3 (D) P-4, Q-1, R-3, S-2

20. A coastal city produces municipal solid waste (MSW) with high moisture content,
high organic materials, low calorific value and low inorganic materials. The most
effective and sustainable option for MSW management in that city is
(A) Composting (B) Dumping in sea (C) Incineration (D) Landfill

21. According to the Noise Pollution (Regulation and control) Rules, 2000, of the
Ministry of Environment and Forests, India, the day time and night time noise
level limits in ambient air for residential areas expressed in dB(A) Leg are
(A) 50 and 40 (B) 55 and 45 (C) 65 and 55 (D) 75 and 70

22. An air parcel having 40ºC temperature moves from ground level to 500m
elevation in dry air following the “adiabatic lapse rate”. The resulting temperature
of air parcel at 500m elevation will be
(A) 35ºC (B) 38ºC (C) 41ºC (D) 44ºC

23. Aggregate impact value indicates the following property of aggregates
(A) Durability (B) Toughness (C) Hardness (D) Strength

24. As per IRC: 67-2001, a traffic sign indicating the Speed Limit on a road should be
of
(A) Circular Shape with White Background and Red Border
(B) Triangular Shape with White Background and Red Border
(C) Triangular Shape with Red Background and White Border
(D) Circular Shape with Red Background ad White Border

25. The local mean time at a place located in longitude 90º 40’E when the standard
time is 6 hours and 30 minutes and the standard meridian is 82º 30’E is
(A) 5 hours, 2 minutes and 40 seconds
(B) 5 hours, 57 minutes and 20 seconds
(C) 6 hours, and 30 minutes
(D) 7 hours, 02 minutes and 40 seconds



Q. No. 26 – 51 Carry Two Marks Each

d2 y dy
26. The solution to the ordinary differential equation + − 6y = 0 is
dx2 dx
(A) y = c1e3x + c2 e−2x (B) y = c1e3x + c2e2x

(C) y = c1e−3x + c2e2x (D) y = c1e−3x + c2e−2x

⎡3 + 2i i ⎤
27. The inverse of the matrix ⎢ ⎥ is
⎣ − i 3 − 2i⎦
1 ⎡3 + 2i −i ⎤ 1 ⎡3 − 2i −i ⎤
(A) (B)
12 ⎢ i
⎣
⎥
3 − 2i⎦ 12 ⎢ i
⎣
⎥
3 + 2i⎦

1 ⎡3 + 2i −i ⎤ 1 ⎡3 − 2i −i ⎤
(C) ⎢ ⎥ (D) ⎢ ⎥
14 ⎣ i 3 − 2i⎦ 14 ⎣ i 3 + 2i⎦

28. The table below gives values of a function F(x) obtained for values of x at
intervals of 0.25.

x 0 0.25 0.5 0.75 1.0
F(x) 1 0.9412 0.8 0.64 0.50

The value of the integral of the function between the limits 0 to 1 using
Simpson’s rule is
(A) 0.7854 (B) 2.3562 (C) 3.1416 (D) 7.5000

29. The partial differential equation that can be formed from
⎛ ∂z ∂z ⎞
z = ax + by + ab has the form ⎜ with p = and q = ⎟
⎝ ∂x ∂y ⎠
(A) z=px+qy (B) z=px+pq (C) z=px+qy+pq (D) z=qy+pq

30. A parabolic cable is held between two supports at the same level. They horizontal
span between the supports is L. The sag at the mid-span is h. The equation of
x2
the parabola is y = 4h 2 , where x is the horizontal coordinate and y is the
L
vertical coordinate with the origin at the centre of the cable. The expression for
the total length of the cable is
L L /2
h2 x2 h3 x2
(A) ∫
0
1 + 64
L4
dx (B) 2 ∫
0
1 + 64
L4
dx

L /2 L /2
h2 x2 h2 x2
(C) ∫
0
1 + 64
L4
dx (D) 2 ∫
0
1 + 64
L4
dx



31. Given a function
f ( x, y ) = 4x2 + 6y2 − 8x − 4y + 8

The optimal value of f(x, y)
(A) Is a minimum equal to 10/3 (B) Is a maximum equal to 10/3
(C) Is a minimum equal to 8/3 (D) Is a maximum equal to 8/3

32. A double cover butt riveted joint is used to connect two flat plates of 200mm
width and 14mm thickness as show in the figure. There are twelve power driven
rivets of 20mm diameter at a pitch of 50mm in both directions on either side of
the plate. Two cover plates of 10mm thickness are used. The capacity of the joint
in tension considering bearing and shear ONLY, with permissible bearing and
shear stresses as 300MPa respectively is

50mm 50mm 50mm
50mm

50mm

50mm

50mm

(A) 1083.6kN (B) 871.32kN (C) 541.18kN (D) 433.7kN

33. Two plates, subjected to direct tension, each of 10mm thickness and having
widths of 100mm and 175mm, respectively are to be fillet welded with an overlap
of 200mm. Given that the permissible weld stress is 110MPa and the permissible
stress in steel is 150MPa, then length of the weld required using the maximum
permissible weld size as per IS: 800-1984 is

100mm 175mm

200mm

(A) 245.3mm (B) 229.2mm (C) 205.5mm (D) 194.8mm



34. For the simply supported beam of length L, subjected to a uniformly distributed
moment M kN-m per unit length as shown in the figure, the bending moment (in
kN-m) at the mid-span of the beam is

M kN - m per unit length

L

(A) Zero (B) M (C) ML (D) M/L

35. A disc of radius r has a hole of radius r cut-out as shown. The centroid of the
2
remaining disc (shaded portion) at a radial distance from the centre “O” is

r /2

'O'

O

r

r r r r
(A) (B) (C) (D)
2 3 6 8
36. A three hinged parabolic arch having a span of 20m and a rise of 5m carries a
point load of 10kN at quarter span from the left end as shown in the figure. The
resultant reaction at the left support and its inclination with the horizontal are
respectively
10kN

5m

5m 5m 10m

(A) 9.01kN and 56.31º (B) 9.01kN and 33.69º
(C) 7.50kN and 56.31º (D) 2.50kN and 33.69º



37. The vertical stress at point P1 due to the point load Q on the ground surface as
shown in figure is s2. According to Boussinesq’s equation, the vertical stress at
point P2 shown in figure will be
Q

z
2
z P2
r
2

P1
r

σz
(A) (B) σz (C) 2σz (D) 4σz
2

38. An open ended steel barrel of 1m height and 1m diameter is filled with saturated
fine sand having coefficient of permeability of 10−2 m / s . The barrel stands on a
saturated bed of gravel. The time required for the water level in the barrel to
drop by 0.75m is
(A) 58.9s (B) 75s (C) 100s (D)150s

39. The ultimate load capacity of a 10m long concrete pile of square cross section
500mm x 500mm driven into a homogeneous clay layer having undrained
cohesion value of 40kPa is 700kN. If the cross section of the pile is reduced to
250mm x 250mm and the length of the pile is increased to 20m, the ultimate
load capacity will be
(A) 350kN (B) 632.5kN (C) 722.5kN (D) 1400kN

40. For a rectangular channel section, Group I lists geometrical elements and Group
II gives proportions for hydraulically efficient section.

Group I Group II
ye
P Top width 1
2
Q Perimeter 2 ye

R Hydraulic Radius 3 2 ye

S Hydraulic Depth 4 4 ye

ye is the follow depth corresponding to hydraulically efficient section. The correct
match of Group I with Group II is
(A) P-2, Q-4, R-1, S-3 (B) P-3,Q-1,R-4,S-2
(C) P-3,Q-4,R-1,S-2 (D) P-3,Q-4,R-2,S-1


41. The Froude number of flown in a rectangular channel is 0.8. If the depth of flow
is 1.5m, the critical depth is
(A) 1.80m (B) 1.56m (C) 1.36m (D) 1.29m

42. A wall of diameter 20cm fully penetrates a confined aquifer. After a long period of
pumping at a rate of 2720litres per minute, the observations of drawdown taken
at 10m and 100m distances from the center of the wall are found to be 3m and
0.5m respectively. The transmissivity of the aquifer is
(A) 676m2/day (B) 576 m2/day (C) 526 m2/day (D) 249 m2/day

43. If the BOD3 of a wastewater sample is 75mg/L and reaction rate constant k
(base e) is 0.345 per day, the amount of BOD remaining in the given sample
after 10days is
(A) 3.21 mg/L (B) 3.45 mg/L (C) 3.69 mg/L (D) 3.92 mg/L

44. Consider the following statements in the context of geometric design of roads.
I: A simple parabolic curve is an acceptable shape for summit curves.
II: Comfort to passengers is an important consideration in the design of summit
curves.
The correct option evaluating the above statements and their relationship is
(A) I is true, II is false
(B) I is true, II is true, and II is the correct reason for I
(C) I is true, II is true, and II is NOT the correct reason for I
(D) I is false, II is true

45. The design speed for a two-lane road is 80kmph. When a design vehicle with a
wheelbase of 6.6m is negotiating a horizontal curve on that road, the off-tracking
is measured as 0.096m. The required widening of carriageway of the two-lane
road on the curve is approximately
(A) 0.55m (B) 0.65m (C) 0.75m (D) 0.85m

46. Consider the following statements in the context of cement concrete pavements.
I. Warping stresses in cement concrete pavements are caused by the seasonal
variation in temperature.
II. Tie bars are generally provided across transverse joints of cement concrete
pavements
The correct option evaluating the above statements is
(A) I: True II: False (B) I: False II: True
(C) I: True II: True (D) I: False II: False



47. A bench mark has been established at the soffit of an ornamental arch at the
known elevation of 100.0m above sea level. The back sight used to establish
height of instrument is an inverted staff reading of 2.105m. A forward sight
reading with normally held staff of 1.105m is taken on a recently constructed
plinth. The elevation of the plinth is
(A) 103.210m (B) 101.000m (C) 99.000m (D) 96.790m

Common Data Questions: 48 & 49

Ion concentrations obtained for a groundwater sample (having pH=8.1) are given
below.

Ion Ca2+ Mg2+ Na+ HCO3- SO42- Cl-
Ion 100 6 15 250 45 39
concentration
(mg/L)
Atomic Weight Ca=40 Mg=24 Na=23 H=1, S=32, Cl=35.5
C=12, O=16
O=16

48. Total hardiness (mg/L as CaCO3) present in the above water sample is
(A) 205 (B) 250 (C) 275 (D) 308

49. Carbonate hardness (mg/L as CaCO3) present in the above water sample is
(A) 205 (B) 250 (C) 275 (D) 289

Common Data Questions: 50 & 51

The moisture holding capacity of the soil in a 100 hectare farm is 18cm/m. the field is to
be irrigated when 50 percent of the available moisture in the root zone is depleted. The
irrigation water is to be supplied by a pump working for 10hours a day, and water
application efficiency is 75%. Details of crops planned for cultivation are as follows:

Peak rate of moisture use
Crop Root zone depth (m)
(mm/day)
X 1.0 5.0

Y 0.8 4.0

50. The capacity of irrigation system required to irrigate crop X in 36 hectares is
(A) 83litres/sec (B) 67 liters/sec (C) 57 liters/sec (D) 53 liters/sec



51. The area of crop Y that can be irrigated when the available capacity of irrigation
system is 40 liters / sec is
(A) 40hectares (B) 36 hectares (C) 30 hectares (D) 27 hectares

Linked Answer Questions 52 & 53

A doubly reinforced rectangular concrete beam has a width of 300mm and an effective
depth of 500mm. the beam is reinforced with 2200mm2 of steel in tension and 628mm2
of steel in compression. The effective cover for compression steel is 50mm. Assume that
both tension and compression steel yield. The grades of concrete and steel used are M20
and Fe250 respectively. The stress lock parameters (rounded off to first two decimal
places) for concrete shall be as per IS 456:200.

52. The depth of neutral axis is
(A) 205.30mm (B) 184.56mm (C) 160.91mm (D) 145.30mm

53. The moment of resistance of the section is
(A) 206.00kN-m (B) 209.20 kN-m (C) 236.80 kN-m (D) 251.90kN-m,

Statement for Linked Answer Questions: 54 & 55

The unconfined compressive strength of a saturated clay sample is 54kPa.

54. The value of cohesion for the clay is
(A) zero (B) 13.5kPa (C) 27kPa (D)54kPa

55. If a square footing of size 4m x 4m is resting on the surface of a deposit of the
above clay, the ultimate bearing capacity of the footing (as per Terzaghi’s
equation) is
(A) 1600kPa (B) 315kPa (C) 27kPa (D)54kPh

Q. No. 56 – 60 Carry One Mark Each

56. Which of the following options is closest in meaning to the word Circuitous.
(A) cyclic (B) indirect (C) confusing (D) crooked

57. The question below consists of a pair of related words followed by four pairs of
words. Select the pair that best expresses the relation in the original pair.
Unemployed: Worker
(A) fallow: land (B) unaware: sleeper
(C) wit: jester (D) renovated: house



58. Choose the most appropriate word from the options given below to complete the
following sentence:
If we manage to ____________ our natural resources, we would leave a better
planet for our children.
(A) uphold (B) restrain (C) cherish (D) conserve

59. Choose the most appropriate word from the options given below to the complete
the following sentence:
His rather casual remarks on politics ___________ his lack of seriousness about
the subject.
(A) masked (B) belied (C) betrayed (D)suppressed

60. 25 persons are in a room. 15 of them play hockey, 17 of them play football and
10 of them play both hockey and football. Then the number of persons playing
neither hockey nor football is:
(A) 2 (B)17 (C)13 (D) 3

Q. No. 61 – 65 Carry Two Marks Each

61. Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters).
All were born on 1st January. The age difference between any two successive
siblings (that is born one after another) is less than 3 years. Given the following
facts:
i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age
ii. The age difference between Gita and Saira is 1 year. However Gita is not the
oldest and Saira is not the youngest.
iii. There are no twins.
In what order were they born (oldest first)?
(A) HSIG (B) SGHI (C) IGSH (D) IHSG

62. 5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a
wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2
skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the
wall?
(A) 20 (B) 18 (C) 16 (D) 15

63. Modern warfare has changed from large scale clashes of armies to suppression of
civilian populations. Chemical agents that do their work silently appear to be
suited to such warfare; and regretfully, there exist people in military
establishments who think that chemical agents are useful tools for their cause.



Which of the following statements best sums up the meaning of the above
passage:
(A) Modern warfare has resulted in civil strife.
(B) Chemical agents are useful in modern warfare.
(C) Use of chemical agents in warfare would be undesirable
(D) People in military establishments like to use chemical agents in war.

64. Given digits 2,2,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000
can be formed?
(A) 50 (B) 51 (C) 52 (D) 54

65. If 137+276=435 how much is 731+672?
(A) 534 (B) 1403 (C) 1623 (D)1513


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